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High-quality 3D image recognition is an important component of many vision and robotics systems. However, the accurate processing of these images requires the use of compute-expensive 3D Convolutional Neural Networks (CNNs). To address this challenge, we propose the use of Spiking Neural Networks (SNNs) that are generated from iso-architecture CNNs and trained with quantization-aware gradient descent to optimize their weights, membrane leak, and firing thresholds. During both training and inference, the analog pixel values of a 3D image are directly applied to the input layer of the SNN without the need to convert to a spike-train. This significantly reduces the training and inference latency and results in high degree of activation sparsity, which yields significant improvements in computational efficiency. However, this introduces energy-hungry digital multiplications in the first layer of our models, which we propose to mitigate using a processing-in-memory (PIM) architecture. To evaluate our proposal, we propose a 3D and a 3D/2D hybrid SNN-compatible convolutional architecture and choose hyperspectral imaging (HSI) as an application for 3D image recognition. We achieve overall test accuracy of 98.68, 99.50, and 97.95% with 5 time steps (inference latency) and 6-bit weight quantization on the Indian Pines, Pavia University, and Salinas Scene datasets, respectively. In particular, our models implemented using standard digital hardware achieved accuracies similar to state-of-the-art (SOTA) with ~560.6× and ~44.8× less average energy than an iso-architecture full-precision and 6-bit quantized CNN, respectively. Adopting the PIM architecture in the first layer, further improves the average energy, delay, and energy-delay-product (EDP) by 30, 7, and 38%, respectively.